Pith Number

pith:TZ3BZ3M6

pith:2024:TZ3BZ3M6AHXSOIUDWPONZCW3KG

not attested not anchored not stored refs pending

Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium

Christian Kroer, Luofeng Liao

arxiv:2402.02303 v6 · 2024-02-04 · math.ST · cs.GT · econ.EM · stat.AP · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZ3BZ3M6AHXSOIUDWPONZCW3KG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T10:27:07.204159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e761ced9e01ef272283b3dcdc8adb51b79672ffc4baa6ca7fcee151293328b9

Aliases

arxiv: 2402.02303 · arxiv_version: 2402.02303v6 · doi: 10.48550/arxiv.2402.02303 · pith_short_12: TZ3BZ3M6AHXS · pith_short_16: TZ3BZ3M6AHXSOIUD · pith_short_8: TZ3BZ3M6

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TZ3BZ3M6AHXSOIUDWPONZCW3KG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9e761ced9e01ef272283b3dcdc8adb51b79672ffc4baa6ca7fcee151293328b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1b765c9248a03a1ed1043152776417d7d271a0ca71ea59ddb1d50532d023caf",
    "cross_cats_sorted": [
      "cs.GT",
      "econ.EM",
      "stat.AP",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2024-02-04T00:00:00Z",
    "title_canon_sha256": "648e76d3f23c717efd45f0a97f42fcb4b71eedf22aa865c2837a55433d556061"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.02303",
    "kind": "arxiv",
    "version": 6
  }
}